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Using Delaunay tringles to build desire lines

Using Delaunay tringles to build desire lines. Pedro Camargo, Ph.D. Raleigh, May 17 th , 2017. Traditional desire lines. Implemented in all commercial modelling packages Direct connection between all OD pairs (complete graph) Number of lines on the map: Centroids²

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Using Delaunay tringles to build desire lines

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  1. Using Delaunay tringles to build desire lines Pedro Camargo, Ph.D. Raleigh, May 17th, 2017

  2. Traditional desire lines • Implemented in all commercial modelling packages • Direct connection between all OD pairs (complete graph) • Number of lines on the map: Centroids² • Maps grow too crowded fast

  3. Searching for an alternative • How can to minimize the number of lines? • What if we could get lines that do not overlap? • Why not performing an All-or-Nothing on the network? • A network is not always available • hardly feasible for non-modellers • Can we create a minimal network connecting points of origin and destination? • Yes: Proximity graphs

  4. Proximity graphs • Any two nodes in a given set are connected if and only if the vertices satisfy certain geometric requirements (e.g. distance) • Delaunay triangulation • Gabriel graph • Relative Neighborhood graphs • Minimum Spanning Tree • Perturbed Minimum Spanning Tree • Disjoint Minimum Spanning Tree • Etc. Image credit to Matthias Beck, SFSU - http://math.sfsu.edu/beck/teach/870/brendan.pdf

  5. Delaunay triangles Delaunay triangulation DT for a set of points N in a plane is a triangulation for which no point in N is enclosed by any triangulation in DT(N) such that the minimum angle of all the angles of the triangles in DT(N) is maximized • It is unique • Fast computation, with complexity of O(n log logn)

  6. The algorithm • Compute the Delaunay triangulation for a set of centroids (areas, zones, etc.) • Interpret the edges of the Delaunay Triangles as bi-directional links • Build a graph based on the set of links generated • Perform an All-or-Nothing assignment on the graph • Return the Delaunay Triangulation links with flows per direction to the user.

  7. Implementation • Python code • Scipy (Delaunay triangulation) • AequilibraE (Traffic assignment) • QGIS interface • Within AequilibraE (Version 0.3 and greater)

  8. Interface

  9. AequilibraE • Open source transportation modelling platform • Python API • QGIS plugin with GUI for computation • Features • Network manipulation • Path computation/assignment • Trip Distribution • Desire lines • Bandwidth mapping, etc.

  10. Example: USA (Migration) • American community Survey migration database • County-to-county migration flows • ~3,200 counties

  11. Example: USA (Migration) Flows > 1,000

  12. Example: USA (Migration)

  13. Example: FAF (USA) • Freight Analysis Framework • Commodity based freight model • Currently in its 4th generation • 43 commodities • 132 Zones (released. Modelled at county level: ~3.000) • 5 modes (truck, rail, water, air, pipeline) • Three scenarios: low, medium and high • Future year scenarios every 5 years through 2045

  14. Example: FAF (USA) 85% of flows

  15. Example: FAF (USA)

  16. Example: Brazil (Freight model) • National Plan of Transportation and Logistics (PNLT) • Commodity based freight model • Currently in its 3rd generation • 28 commodities • 523 zones • 4 modes (truck, rail, water, pipeline) • Three scenarios: Low, medium and high • Future year scenarios every 5 years through 2035

  17. Example: Brazil (Freight model) 85% of flows

  18. Example: Australia • Road freight movements • Commodity based survey • 2014 calendar year data • Previous survey included all modes • 22 commodities + empty trucks • 5 transport methods ( container, liquid bulk, solid bulk, other freight + not specified) • 351 zones (SA3)

  19. Example: Australia (Southeast Queensland)

  20. Example: Australia (Southeast Queensland)

  21. How reasonable are the results • Are paths through the Delaunay network significantly longer than their direct counterparts? • Upper bound of the “cost” increase: (+142%) • Typical increase • USA (Migration): 1.041 (4.1%) • USA (FAF3): 1.094 (+ 9.4%) • Brazil (PNLT): 1.057 (+ 5.7%) • Australia: (SA3): 1.0135 (+ 1.35%)

  22. Final thoughts • Re-interpreting desire lines in the form of Delaunay Lines makes them useful again • On the implementation: • Open source • User friendly • Efficient • Further research into alternative minimal networks might prove fruitful

  23. Thank you! Professional Pedro.Camargo@veitchlister.com.au www.veitchlister.com.au www.linkedin.com/in/pedrocamargo Personal c@margo.co www.xl-optim.com @pedrocamargo

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